Related papers: Measuring Sample Quality with Stein's Method
In this paper we study asymptotic properties of different data-augmentation-type Markov chain Monte Carlo algorithms sampling from mixture models comprising discrete as well as continuous random variables. Of particular interest to us is…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…
Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is post-processed and…
Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…
A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.
Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…
We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of…
This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed…
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
Metrics of model goodness-of-fit, model comparison, and model parameter estimation are the main categories of statistical problems in science. Bayesian and frequentist methods that address these questions often rely on a likelihood…
The paper presents an investigation of estimating treatment effect using different matching methods. The study proposed a new method which is computationally efficient and convenient in implication-'largest caliper matching' and compared…
Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…